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Angle in a Semi-circle Proof

Angle in a Semi-circle Proof
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2015-01-13 16:01
CircleAngleCoordinate GeometryGeometric Construction
In collections Circle Theorems
This example demonstrates the geometric theorem that the angle subtended by a diameter in a circle is a right angle. It involves core concepts like circles, triangles, angles, and coordinate geometry. The construction uses GeoGebra commands and objects such as Circle, Line, Intersect, Segment, Point, and Angle. Suitable for high school mathematics students to learn about circle properties and geometric proofs, as well as for teaching coordinate geometry.

GeoGebra Commands & Parameters

  1. Circle(O, B) → c
  2. Line(O, B) → a
  3. Intersect(c, a, 2) → A
  4. Segment(A, B) → b
  5. Point(c) → D
  6. Segment(A, D) → d
  7. Segment(D, B) → e
  8. Segment(O, D) → f
  9. Segment(A, O) → g
  10. Angle(O, A, D) → α
  11. Angle(A, D, O) → β
  12. Angle(O, D, B) → γ
  13. Angle(D, B, O) → δ
  14. Segment(O, B) → h
  15. Segment(O, D) → j